Exact quantum state for N=1 supergravity

TL;DR

This paper derives the exact quantum state for N=1 supergravity in four dimensions, demonstrating the closure of the algebra of symmetry generators and providing an explicit solution to all quantum constraints.

Contribution

It presents the first explicit exact quantum solution for N=1 supergravity in 3+1 dimensions, including the algebra of all symmetry generators.

Findings

Algebra of generators closes in the chosen operator ordering.

Explicit quantum state satisfying all constraints is obtained.

Generalization of previous Bianchi-type models ansatz to full supergravity.

Abstract

For N=1 supergravity in 3+1 dimensions we determine the graded algebra of the quantized Lorentz generators, supersymmetry generators, and diffeo-morphism and Hamiltonian generators and find that, at least formally, it closes in the chosen operator ordering. Following our recent conjecture and generalizing an ansatz for Bianchi-type models we proposed earlier we find an explicit exact quantum solution of all constraints in the metric representation.